Abstract
This paper proposes a new model of facility location problem referred to as k-product uncapacitated facility location problem with multi-type clients. The k-product uncapacitated facility location problem with multi- type clients consists of two set of sites, one is the set of demand points where clients are located and the other is the set of sites where facilities of unlimited capacities can be set up to serve the clients. Each facility can provide only one kind of products. Each client needs to be served by a set of facilities depending on which products it needs. Each facility can be set up only for one of the k products with a non-negative fixed cost determined by the product it is designated to provide. There is also a nonnegative cost of shipping goods between each pair of locations. The problem is to determine the set of facilities to be set up and to find an assignment of each client to a set of facilities so that the sum of the setup costs and the shipping costs is minimized. Under the assumption that the setting costs is zero and the shipping costs are in facilities centered metric space, it is shown that the problem with two kinds of clients is NP-complete. Furthermore a heuristic algorithm with worst case performance ratio not more than 2-1/k is presented for any integer k.
Highlights
In the last few years, a number of constant factor approximation algorithms have been proposed for facility location problem when the service cost is assumed to be in the metric space by Ageev [1], Chudak and Shmoys [2], Guha & Khuller [3], Mahdian et al [4], Shmoys et al [5] and Zhang [6]
This paper proposes a new model of facility location problem referred to as k-product uncapacitated facility location problem with multi-type clients
The k-product uncapacitated facility location problem with multitype clients consists of two set of sites, one is the set of demand points where clients are located and the other is the set of sites where facilities of unlimited capacities can be set up to serve the clients
Summary
In the last few years, a number of constant factor approximation algorithms have been proposed for facility location problem when the service cost is assumed to be in the metric space by Ageev [1], Chudak and Shmoys [2], Guha & Khuller [3], Mahdian et al [4], Shmoys et al [5] and Zhang [6]. In the classical simple uncapacitated facility location problem, each client only needs one kind of product. Each client needs to be supplied with k kinds of products by a set of k different facilities and each facility can be set up to supply only a distinct product with a non-negative fixed cost determined by the product it intends to supply
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
